Carrying capacity Carrying capacity is typically defined as the maximum population size that can be supported indefinitely by a given environment. The simplicity of this definition belies the complexity of the concept and its application. There are at least four closely related uses of the term in basic ecology, and at least half a dozen additional definitions in applied ecology. Basic Ecology Carrying capacity is most often presented in ecology textbooks as the constant K in the logistic population growth equation, derived and named by Pierre Verhulst in 1838, and rediscovered and published independently by Raymond Pearl and Lowell Reed in 1920: where N is the population size or density, r is the intrinsic rate of natural increase (i.e., the maximum per capita growth rate in the absence of competition), t is time, and a is a constant of integration defining the position of the curve relative to the origin. The expression in brackets in the differential form is the density-dependent unused growth potential, which approaches 1 at low values of N, where logistic growth approaches exponential growth, and equals 0 when N=K, where population growth ceases. That is, the unused growth potential lowers the effective value of r (i.e., the per capita birth rate minus the per capita death rate) until the per capita growth rate equals zero (i.e., births=deaths) at K. The result is a sigmoid population growth curve (Figure 1). Despite its use in ecological models, including basic fisheries and wildlife yield models, the logistic equation is highly simplistic and much more of heuristic than practical value; very few populations undergo logistic growth. Nonetheless, ecological models often include K to impose an upper limit on the size of hypothetical populations, thereby enhancing mathematical stability. [Of historical interest is that neither Verhulst nor Pearl and Reed used ‘carrying capacity’ to describe what they called the maximum population, upper limit, or asymptote of the logistic curve. In reality, the term ‘carrying capacity’ first appeared in range management literature of the late 1890s, quite independent of the development of theoretical ecology. Carrying capacity was not explicitly associated with K of the logistic model until Eugene Odum published his classic textbook Fundamentals of Ecology in 1953.] The second use in basic ecology is broader than the logistic model and simply defines carrying capacity as the equilibrial population size or density where the birth rate equals the death rate due to directly density dependent processes. The third and even more general definition is that of a time. In this case, the birth and death rates are not always equal, and there may be both immigration and emigration (unlike the logistic equation), yet despite population fluctuations, the long-term population trajectory through time has a slope of zero. The fourth use is to define carrying capacity in terms of Justus Liebig’s 1855 law of the minimum that population size is constrained by whatever resource is in the shortest supply. This concept is particularly difficult to apply to natural populations due to its simplifying assumptions of independent limiting factors and population size being directly proportional to whatever factor is most limiting. Moreover, unlike the other three definitions, the law of the minimum does not necessarily imply population regulation. Note that none of these definitions from basic ecology explicitly acknowledges the fact that the population size of any species is affected by interactions with other species, including predators, parasites, diseases, competitors, mutualists, etc. Given that the biotic environment afforded by all other species in the ecosystem typically varies, as does the abiotic environment, the notion of carrying capacity as a fixed population size or density is highly unrealistic. Additionally, these definitions of carrying capacity ignore evolutionary change in species that may also affect population size within any particular environment. B A Fig: Logistic growth curve and carrying capacity: A: From Peter Stiling; B: From Ricklefs & Miller Applied Ecology: The term carrying capacity may have first appeared in an 1898 publication by H. L. Bentley of the United States Department of Agriculture, with an original focus on. maximizing production of domestic cattle on rangelands of the US southwest. The first use in wildlife management was apparently associated with classic studies of deer populations on the Kaibab Plateau in northern Arizona in the 1920s. The concept was popularized in wildlife ecology by Aldo Leopold and Paul Errington in the 1930s. There have been four typical uses of carrying capacity in applied ecology, illustrated in Figure 2: (1) the maximal steady-state number or biomass of animals an area can support in the absence of exploitation (the original use of carrying capacity, K); (2) the maximal sustainable yield (MSY) of biomass of animals an area can produce for exploitation, which equals 0.5K in the simplest form of the logistic model; (3) the maximal sustainable economic yield (MEY) of animals an area can produce for exploitation, which equals the maximum difference between yield value and cost of exploitation; and (4) the open-access equilibrium (OAE), where the value of the yield equals the cost of exploitation, which is the upper economic limit of exploitation in the absence of economic subsidies and restrictive management regulations. Note that open access, typical of historical marine fisheries, often leads to severe overexploitation because the population is reduced to sizes far below the other types of carrying capacity. Indeed, even the application of maximum sustainable yield in single species fisheries management has proven elusive and often disastrous, as evidenced by the poor state of most marine fishery stocks so managed. Two additional uses of carrying capacity in applied ecology focus on optimal stocking of rangeland with cattle, sheep, etc. The Society for Range Management defines the term as the maximum stocking rate possible which is consistent with maintaining or improving vegetation or related resources. A more general definition is the optimum stocking level to achieve specific objectives given specified management options. These practical definitions implicitly acknowledge that carrying capacity is not a constant, but rather is affected by a variety of environmental factors. ECONOMIC CARRYING CAPACITY Economic carrying capacity is defined by management goals for population productivity, animal quality and habitat conditions but is determined by a habitat’s variable and limited ability to sustain achievement of these goals. Economic carrying capacities defined by management goals for population productivity and for population control are termed maximum harvest density and minimum impact density. Maximum harvest density The concept is usually applicable to ungulates. It is the number of animals that a habitat will support while producing a maximum sustained harvestable surplus. In terms of the sigmoid model, the population is at or somewhat above the inflection point. The population must be maintained at this level of abundance by harvest. Therefore no lack of welfare factors prohibit the growth of a population Impact on wildlife populations & its habitat 1. At maximum harvest density, population quality will be very good though not probably the very best possible. 2. Populations at MHD characteristically exhibit a young age structure and high rate of turnover 3. Habitat condition will also be good though not without signs of use and perhaps retrogressed vegetation Minimum impact density Minimum impact density as a goal for wildlife management aims to reduce the impact of wild animals on those of desirable target species. It may be desirable to maintain a population at MID of carrying capacity if - The population is considered to be a pest species, one not to be eliminated but to be controlled - The predator population depresses the production of livestock or desirable wildlife species - Ungulates compete with valuable and perhaps less competitive wildlife species target of a particular management programme Impact on wildlife population and its habitat 1. Populations maintained at Minimum impact density of carrying capacity have a very low level of ecological density. 2. Reproduction and resistance to natural mortality is generally high in such populations, requiring persistent and abundant harvest of animals to maintain the population at this level. 3. The population habitat should also be in excellent condition, receiving only minor use from the depressed population. “Ecological carrying capacity is a variable habitat characteristic determined by changeful amounts of welfare factors that limit the size and productivity of a species population.” Sometimes populations are unharvested, or normal levels of harvest do not influence the population size very much. In these cases carrying capacities are determined only by limiting habitat resources, and it is often useful to distinguish which set of limiting resources is important in determining population size. Ecological carrying capacity as determined by limiting amount of forage or interspersion and of space is termed as subsistence density, security density and tolerance density respectively. Subsistence density It is the size of an unharvested population limited primarily by forage. In terms of the sigmoid model subsistence density occurs at the upper asymptote. Impact on wildlife population